derivative y=2\sqrt[3]{x}

解答

导数

y = 2 3 x

\frac{2}{3 x ^{\frac{2}{3}}}

求解步骤

\frac{d}{d x} (2 3 x)

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (3 x)

使用根式运算法则:

n a = a^{\frac{1}{n}}

= 2 \frac{d}{d x} (x^{\frac{1}{3}})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

化简

2 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{2}{3 x ^{\frac{2}{3}}}

= \frac{2}{3 x ^{\frac{2}{3}}}

t an g e n t y = (1 + 4 x)^{11}, (0, 1)

t an g e n t f (x) = \frac{x}{x + 6}, at x = 4

d er i v a t i v e e^{\frac{z}{z - 6}}

\int \frac{16 s - 4}{3 - 2 s + 4 s ^{2}} d s

d er i v a t i v e y = tan (e^{3 t}) + e^{t a n (3 t)}